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On the dynamics of crown structure in simultaneous two droplets impact onto stationary and moving liquid film. (English) Zbl 1390.76031
Summary: We present a numerical study on the dynamic behaviour of two droplets impinging simultaneously onto a liquid film. A high density ratio based lattice Boltzmann method is employed for the present two-phase computations. Formation of a central uprising jet is observed due to the collision and coalescence of in between rims caused by the impacting droplets. Effect of separation gap between the droplets, film thickness, viscosity and gas density on the crown structure and jet behaviour are systematically studied. The influence of a moving wall with a liquid film on the jet behaviour is further investigated. It is shown that for a larger separation gap between the droplets, a delay in formation of central jet is observed while the spread length increases. For the thin films, the central jet height increases with the film thickness, however a reversal in this behaviour is observed for the thicker films. The rate of increase of jet height and spread length is found to decrease with increase in gas density. Effect of wall velocity is found to enhance the upstream jet, while it suppresses the central and the downstream jets.

76A20 Thin fluid films
76T10 Liquid-gas two-phase flows, bubbly flows
76D99 Incompressible viscous fluids
76M28 Particle methods and lattice-gas methods
Full Text: DOI
[1] Worthington, A. M., A study of splashes, (1908), Longmans, Green and Co
[2] Bhaga, D.; Weber, M. E., Bubbles in viscous liquid: shapes, wakes and velocities, J Fluid Mech, 106, 61-85, (1981)
[3] Cossali, G. E.; Coghe, A.; Marengo, M., The impact of a single drop on a wetted solid surface, Exp Fluids, 22, 463-472, (1997)
[4] Cossali, G. E.; Marengo, M.; Coghev, A.; Zhdanov, S., The role of time in single drop splash on thin film, Exp Fluids, 36, 888-900, (2004)
[5] Gunstensen, A. K.; Rothman, D. H.; Zaleski, S.; Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys Rev A, 43, 4320-4327, (1991)
[6] Hartunian, R. A.; Sears, W. R., On the instability of small gas bubbles moving uniformly in various liquids, J Fluid Mech, 3, 27-47, (1957) · Zbl 0079.44405
[7] He, Xiaoyi; Shan, Xiaowen; Zhang, Raoyang, A lattice Boltzmann scheme for incompressible multiphase flow and its application insimulation of Rayleigh Taylor instability, J Comput Phys, 152, 642-663, (1999) · Zbl 0954.76076
[8] Hua, Jinsong; Lou, Jing, Numerical simulation of bubble rising in viscous liquid, J Comput Phys, 222, 769-795, (2007) · Zbl 1158.76404
[9] Zheng, H. W.; Shu, C.; Chew, Y. T., A lattice Boltzmann model for multiphase flows with large density ratio, J Comput Phys, 218, 353-371, (2006) · Zbl 1158.76419
[10] Inamuro, T.; Ogata, T.; Tajima, S.; Konishi, N., A lattice Boltzmann method for incompressible two-phase flows with large density differences, J Comput Phys, 198, 628-644, (2004) · Zbl 1116.76415
[11] Jamet, D.; Lebaigue, O.; Coutris, N.; Delhaye, J. M., The second gradient method for the direct numerical simulation of liquid vapor flows with phase change, J Comput Phys, 169, 624-651, (2001) · Zbl 1047.76098
[12] Josserand, C.; Zaleski, S., Droplet splashing on thin film, Phys Fluids, 15, (2003) · Zbl 1186.76263
[13] Randy, L.; Vander Wal, G.; Berger, M.; Mozes, S. D., The role of time in single drop splash on thin film, Exp Fluids, 40, 33-52, (2006)
[14] Lallemand, P.; Luo, L. S., Lattice Boltzmann method for moving boundaries, J Comput Phys, 184, 406-421, (2003) · Zbl 1062.76555
[15] Lamb, H., Hydrodynamics, (1932), Dover New York · JFM 26.0868.02
[16] Lee, T.; Lin, C. L., Pressure evolution lattice Boltzmann-equation method for two phase flow with phase change, Phys Rev E, 67, 056703, (2003)
[17] Lee, T.; Lin, C. L., A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J Comput Phys, 206, 16-47, (2005) · Zbl 1087.76089
[18] Luo, L. S., Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases, Phys Rev E, 63, 4982-4996, (2000)
[19] Swift, M. R.; Osborn, W. R.; Yeomans, J. M., Lattice Boltzmann for simulations for liquid-gas and binary fluid systems, Phys Rev E, 54, 5041-5052, (1996)
[20] Mukherjee, S.; Abraham, J., Crown behavior in drop impact on wet walls, Phys Fluids, 19, (2007) · Zbl 1146.76490
[21] Nikolopoulos, N.; Theodorakakos, A.; Bergeles, G., Normal impingement of a droplet onto a wall film: a numerical investigation, Int J Heat Fluid Flow, 26, 119-132, (2005)
[22] Redapangu, P. R.; Sahu, K. C.; Vanka, S. P., A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach, Phys Fluids, 24, 1-10, (2012)
[23] Redapangu, P. R.; Sahu, K. C.; Vanka, S. P., A lattice Boltzmann simulation of three-dimensional displacement flow of two immiscible liquids in a square duct, J Fluids Eng, 135, (2013)
[24] Redapangu, P. R.; Vanka, S. P.; Sahu, K. C., Multiphase lattice Boltzmann simulations of buoyancy-induced flow of two immiscible fluids with different viscosities, Eur J Mech B/Fluids, 34, 105-114, (2012) · Zbl 1258.76125
[25] Ray, B.; Biswas, G.; Sharma, A., Clsvof method to study consecutive drop impact on liquid pool, Int J Numer Methods Heat Fluid Flow, 23, 143-157, (2013) · Zbl 1356.76255
[26] Rein, M., Phenomena of liquid drop impact on solid and liquid surfaces, Fluid Dyn Res, 12, 61-93, (1993)
[27] Rieber, M.; Frohn, A., A numerical study on the mechanism of splashing, Int J Heat Fluid Flow, 20, 455-461, (1999)
[28] Roisman, I. V.; Prunet-Foch, B.; Tropea, C.; Vignes-Adler, M., Multiple drop impact onto a dry solid substrate, J Colloid Interface Sci, 256, 396-410, (2002)
[29] Roisman, I. V.; Tropea, C., Impact of a drop onto a wetted wall: description of crown formation and propagation, J Fluid Mech, 472, 373-397, (2002) · Zbl 1163.76357
[30] Rothman, D. H.; Keller, J. M., Immiscible cellular-automaton fluids, J Stat Phys, 52, 1119-1127, (1988) · Zbl 1084.82504
[31] Sankaranarayanan, K.; Shan, X.; Kevrekidis, I. G.; Sundaresan, S., Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method, J Fluid Mech, 452, 61-96, (2002) · Zbl 1059.76070
[32] Chen, S.; Doolen, G., Lattice Boltzmann method for fluid flows, Annu Rev Fluid Mech, 30, 329-364, (1998)
[33] Shetabivash, H.; Ommi, F.; Heidarinejad, G., Numerical analysis of droplet impact onto liquid film, Phys Fluids, 26, (2014)
[34] Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo, Simulations of bubble motion under gravity by lattice Boltzmann method, J Nucl Sci Technol, 38, 5, 330-341, (2001)
[35] Tanaka, Y.; Washio, Y.; Yoshino, M.; Hirata, T., Numerical simulation of dynamic behavior of droplet on solid surface by the two-phase lattice Boltzmann method, Comput Fluids, 40, 68-78, (2011) · Zbl 1245.76121
[36] Tong, A. Y.; Kasliwal, S.; Fujimoto, H., On the successive impingement of droplets onto a substrate, Numer Heat Transfer, Part A, 52, 531-548, (2007)
[37] Tripathi, M. K.; Sahu, K. C.; Govindrajan, R., Why a falling drop does not in general behave like a rising bubble, Nature Sci Rep, 4, 4771, (2014)
[38] Weiss, D. A.; Yarin, A. L., Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation, J Fluid Mech, 385, 229-254, (1999) · Zbl 0931.76011
[39] Chen, H.; Shan, X., Lattice Boltzmann for simulating flows with multiple phases and components, Phys Rev E, 47, 3, 1815-1819, (1993)
[40] Yarin, A. L., Drop impact dynamics: splashing, spreading, receding, bouncing, Annu Rev Fluid Mech, 38, 159-192, (2006) · Zbl 1097.76012
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